The object studied in this paper is a pair (Φ, Y ), where Φ is a random surface in and Y a random vector field on . The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector field Y is smooth outside Φ but may have discontinuities on Φ. Gauss' divergence theorem is applied to derive a flow conservation law for Y. For this specializes to a well-known rate conservation law for point processes. As an application, relationships for the linear contact distribution of Φ are derived.
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Last et al. (1996) studied this question.
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